International Journal of Scientific and Research Publications, Volume 4, Issue 10, October 2014
ISSN 2250-3153
1
Zoom FFT Algorithm in Ultrasonic Blood Flow Analysis
Using MATLAB
Shireen Romana *, Prof. Rajendra Chincholi **
*
Dept of BME&II, PDA College of Engineering, Gulbarga, India
**
Dept. of IT, PDA College of Engineering, Gulbarga, India
Abstract- An adequate blood supply is required for the normal
functioning of all organs in the body. However this flow can be
impeded due to several reasons, thrombus or clot being a major
one. Detection of such clots is done with the help of an imaging
technique called “DOPPLER ULTRASONOGRAPHY” by
transmitting an ultrasound pulse and calculating the frequency of
the received signal. If there is no clot the reception is always a
homogenous signal, whereas if a certain part being sonographed
has a clot the received signal shows a variance in frequency
which depends upon the distance from the receiver. Hence blood
clot detection in ultrasonography is based on obtaining the
frequency variance and applying adaptive thresholding.In this
work we propose a ZOOM FFT based technique followed by
automated adaptive thresholding to detect the clot. Data files are
synthesized by simulation in MATLAB. Also the entire system is
developed in a Matlab environment for the system to be both
simple and cost-effective.
Experimental results show that the accuracy of the system is
very high even under noisy conditions.
Index Terms- Ultrasound, Thrombo-embolism, Doppler Effect,
adaptive thresholding, Zoom FFT
I. INTRODUCTION
B
lood circulation is essential for a healthy body. Every cell in
the body needs to receive oxygen and nutrients. Blood rich
in oxygen is sent to the body organs, tissues and cells to nourish
them, and the waste products that result are disposed off through
the same system. The circulatory system includes several
common disorders among them is Embolism which is a blood
clot that is able to travel. This is dangerous because it could
travel to the brain, lungs or heart. In clinical practice such blood
clots are detected using a technique called Doppler Ultrasound
Imaging.
II. EXISTING SYSTEMS
Blood clotting is currently detected in time domain based
on Doppler delay which is the resonating time of ultrasound
pulse from transmitter to blood surface and back to receiver.
However time domain based analysis suffers from ripple and salt
and pepper noise which affects the accuracy of the system to a
great deal. In order to overcome this drawback a frequencydomain analysis based on FFT is adopted. However FFT-based
techniques cannot detect minute deviations in frequency which
represents minute clots or those present in the deeper vessels.
Therefore we need methods to distinguish the peaks and
existence of any secondary peak which is added by the presence
of a clot. Hence ZOOM FFT technique is proposed.
III. PROPOSED METHOD
Considering the above mentioned requirements, in this
work we propose a novel method called ZOOM FFT with
Adaptive thresholding to automatically detect blood clotting
from Doppler ultrasound signal. We first simulate the ultrasonic
blood flow signal as triangular pulses with sinusoid component
followed by inducing delay based clot signal. FFT of this signal
is filtered using Hanning window and then performing slicing
based main and secondary peak detection.
IV. SYSTEM DESIGN DESCRIPTION
Methodology
I)Basics
“SOUND IS A COMPRESSIONAL WAVE” and is
different from Electromagnetic waves in that it requires a
medium to travel. The frequency spectrum of sound is shown in
figure 7. The audible range of sound lies between 20Hz to 20
KHz. This frequency range of sound is perceivable to humans.
Below this range is called infrasonic and is audible to animals.
Above audible range are Ultrasonic which propagates as a wave
and can travel through different media. Because of this property
ultrasound waves find potential applications in medical and
industrial diagnostics.
II)Doppler effect phenomenon
Whenever an ultrasound wave propagates in a medium it
undergoes various phenomena, the most important is the Doppler
effect which is the basis of many diagnostic applications based
on ultrasound.
The Doppler Effect is the change observed in the
wavelength of sound (and other) waves due to relative motion
between a wave source and a wave receiver. When a wave is
reflected from a moving target, the frequency of the wave
received differs from that which is transmitted. This difference in
frequency is known as the Doppler shift. The amount of increase
or decrease in the frequency depends upon (a) the speed of
motion (b) the angle between the wave direction and the motion
direction, and (c) the frequency of the wave emitted by the
source. The Doppler Effect occurs for any kind of wave but is
commonly experienced in life with sound. This is because speeds
of motion experienced commonly can be a significant fraction of
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International Journal of Scientific and Research Publications, Volume 4, Issue 10, October 2014
ISSN 2250-3153
the speed of sound. With light this is not true and only
astronomical motions provide speeds great enough to produce a
readily observable Doppler effect.
As the ultrasound wave propagates a shift in frequency (f)
of the wave will be expected due to the source and observer’s
motion relative to each other if the distance between them is
reduced or increased. That shift in frequency depends on the
velocity of sound which also depends on density of the medium,
in which it propagates. When a small object is situated in the
path of the sound wave, the wave will be resisted (scattered). A
direct measurement of this velocity will provide useful
information about the dynamic property of the medium. The
Perceived velocity is given by
V’=V-V0
equation 1
In terms of frequency (f), as a velocity dependent factor.
fp = f0 (V+V0)
equation 2
V-Vs
,
for both objects moving towards each other.
fp= fp (V-VO)/ (V+VS)
equation 3
for both objects moving away from each other,
fp : Perceived frequency.
v : velocity of wave.
vs : source velocity.
v0 : velocity of observer.
Thus we get the perceived frequency proportionately
changed with respect to changes in measuring media. The
Doppler Effect can also be explained with respect to pitch or
wavelength, since all are dependent to each other.
The Doppler shift frequency is given by the equationequation (4)
Where fD =Doppler shift,
fe= emitted frequency,
c=speed of sound in tissues,
v= blood flow velocity,
θ= cosine Doppler angle
It is the Doppler shift that Doppler instruments detect.
However, it is the speed of motion or flow of blood in which we
are normally interested. The Doppler equation can be rearranged
in this sense, to place the speed of motion alone on the left side
of the equation.
.
equation 5
The minimum detectable blood flow speed within Doppler
ultrasound is few mm.s-1. The maximum is determined by
aliasing. The range of commonly detected normal flow speeds is
10 to 100 cm.s-1.
V. WHY TO ZOOM?
2
In clinical practice, situations arise wherein the clot in a
vessel may be so small or deeper inside that it induces negligible
frequency shift which is usually not detected with conventional
ultrasonography. However its presence starts to manifest itself
through various symptoms. Under such situations it becomes
important to be able to detect and locate the clot to avoid
undesirable complications and cost of the treatment.
This minute variation in frequency can be seen using Zoom
FFT algorithm.
Zoom fft
The Zoom-FFT is a DSP algorithm which is used to enlarge
a portion of the signal. As the name implies Zoom FFT increases
the frequency resolution of the desired portion of a signal thereby
zooming it so that very fine details in the spectrum can be
visualized. In this process an input signal is mixed down to a
baseband frequency and then decimated, prior to passing it into a
standard FFT. The advantage is for example that if you have a
sample rate of 10 MHz and require at least 10Hz resolution over
a small frequency band (say 1 KHz) then you do not need a 1
Mega point FFT, just decimate by a factor of 4096 and use a 256
point FFT which is obviously quicker.
Zoom-FFT uses digital down conversion techniques to
localize the standard FFT to a narrow band of frequencies that
are centered on a higher frequency. The zoom-FFT is used to
reduce the sample rate required when analyzing narrowband
signals eg. in HF communications.
VI. DESIGN APPROACH
Zoom FFT for blood clot detection is based on detecting
the additional frequency component added by the clot which is
identified as a second prominent peak in the input signal.
The Algorithm can be presented in following steps
1) Take FFT of the Signal
2) Perform Zooming by applying Hanning Window
3) Adjust window parameter to get primary and secondary
peaks.
4) Locate the peak of highest magnitude. Find its width
and location.
5) Find if any other peak exists with amplitude and width
atleast 40% of that of the primary peak.
6) If so then it is recognized as a clot. Amplitude of the
secondary peak gives clotting depth.
7) If no secondary peak is detected then there is no
clotting.
The steps involved in the process are explained below:
Filter
The input signal is filtered using a low pass filter to prevent
aliasing when the signal is subsequently sampled at a lower
sampling rate.
Decimation
Resampling at discrete instances, the already sampled
wave. Decimation is achieved by applying the equation given
below
Minute variations in blood flow can be seen eg. starting
stage of blood clot.
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International Journal of Scientific and Research Publications, Volume 4, Issue 10, October 2014
ISSN 2250-3153
N-1
Y(m)= ∑Scale*x(Mm-k) , M=decimation factor
K=0
Where Scale is the Zooming range and the value is between
0-1
N = number of samples
3
VIII. RESULT
Our system has been tested with normal and abnormal
ultrasound signals under varying noise conditions. A snapshot of
the result is shown in figure1. It is apparent from the results that
our system is capable of detecting clots with negligibly small
magnitudes. It is also observed that the system is least affected
by the presence and amount of noise in the signal.
FFT
The Fast Fourier Transform (FFT) is an algorithm that
efficiently contains the frequency domain conversion. FFT of a
signal is computed using the formula given below
N-1
X(k) = ∑ x(n)e-j2 πnk/N
0<K<N-1
n=0
Where X(K)= FFT of input x(n)
N=number of samples
k = index
Figure 1: snapshot of the result with an ultrasound signal
containing a minute clot along with heavy noise.
Window
After computing FFT of the signal it is windowed. This is
the core part of the Zoom process where zooming is actually
achieved. The window function is used to select a particular
portion of the spectrum. For this work we are using Hanning
window which is a fixed type window defined by the formula
IX. ADVANTAGES
1.
2.
3.
4.
5.
WHN(n)={0.5[1-cos(2πn/M-1)] for n=0 to M-1
0 otherwise
Where M=number of samples
All the above steps are carried out in a single MatLab
program which offers built-in functions for all the steps.
6.
Increased frequency domain resolution
detects the presence of clot at the initial stage itself
Reduced hardware cost and complexity
Wider spectral range
Can be used conveniently by both medical and
paramedical staff
Accurate and reliable
X. CONCLUSION
VII. MATLAB®
MATLAB® is a high-level language and interactive
environment for numerical computation, visualization, and
programming. Using MATLAB, user can analyze data, develop
algorithms, and create models and applications. The language,
tools, and built-in math functions enable the user to explore
multiple approaches and reach a solution faster than with
spreadsheets or traditional programming languages, such as
C/C++ or Java™.
MATLAB can be used for a range of applications,
including signal processing and communications, image and
video processing, control systems, test and measurement,
computational finance, and computational biology. A very
distinct feature of Matlab is the GUI.A graphical user interface
(GUI) is a graphical display in one or more windows containing
controls, called components, that enable a user to perform
interactive tasks. Unlike coding programs to accomplish tasks,
the user of a GUI need not understand the details of how the
tasks are performed.
Currently the project has been tested on the simulation
basis, the output of the simulations are satisfactory.
In the simulation we generated the ultrasound signal with
noise and without noise. Noise is added using AWGN. We take
several signals which includes both normal as well as abnormal
signal. Abnormal signal is generated by adding a delayed signal
with the main signal. We then use Zoom FFT technique to detect
the abnormality. It is shown that we can detect the clotting with
an accuracy of over 90%. The system also gives satisfactory
result under heavy noise.
ACKNOWLEDGMENT
I, Shireen Romana, express my gratitude towards prof.
Rajendra Chincholi and Rupam Das, my co-authors, for their
constant support and dedicated help in completion of this work.
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www.ijsrp.org
International Journal of Scientific and Research Publications, Volume 4, Issue 10, October 2014
ISSN 2250-3153
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AUTHORS
First author- Shireen Romana , M.Tech IVsem, Dept. Of
BME&II, PDA College of Engineering, Gulbarga, India
e-mail: [email protected]
Second author- Rajendra Chincholi, Professor, Dept. of IT,
PDA College of Engineering, Gulbarga, India
Third author- Rupam Das, Integrated Solutions, Gulbarga,
India.
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